Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB${}_2$

Abstract

In 1966 Leggett used a two-band superconductor to show that a new collective mode could exist at low temperatures, corresponding to a counter-flow of the superconducting condensates in each band. Here, the theory of electronic Raman scattering in a superconductor by Klein and Dierker (1984) is extended to a multiband superconductor. Raman scattering creates particle/hole pairs. In the relevant $A_{1g}$\ symmetry, the attraction that produces pairing necessarily couples excitations of superconducting pairs to these p/h excitations. In the Appendix it is shown that for zero wave vector transfer this coupling modifies the Raman response and makes the long-range Coulomb correction null. The 2-band result is applied to MgB${}_2$ where this coupling activates Leggett's collective mode. His simple limiting case is obtained when the interband attractive potential is decreased to a value well below that given by LDA theory. The peak from Leggett's mode is studied as the potential is increased through the theoretical value: With realistic MgB${}_2$\ parameters, the peak broadens through decay into the continuum above the smaller ($\pi$ band) superconducting gap. Finite $q$ effects are also taken into account, yielding a Raman peak that agrees well in energy with the experimental result by Blumberg \textit{et el.} (2007). This approach is also applied to the $q=0$, 2-band model of the Fe-pnictides considered by Chubukov \textit{et al.}(2009).

10 pages, 3 figures. To appear in Physical Review B

References in corpus (3)

• Observation of Leggett's collective mode in a multi-band MgB2 superconductor
• Theory of Raman response in a superconductor with extended s-wave symmetry: Application to Fe-pnictides
• Anharmonicity and self-energy effects of the E2g phonon in MgB2

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